Extended Abstract
Introduction
Site selection for health centers and hospitals in proper locations and the allocation of population to them is an important issue in urban planning. The location and allocation of health and medical facilities including hospitals, have long been an important issue for urban planners that has become more complicated with the growth of population. Location and allocation of hospitals is basically planned to ensure the availability of proper and comprehensive health services as well as the reduction of the establishment costs. Improper planning of the health centers has created multiple problems for big cities in developing countries in recent years. In the present study, the Genetic Algorithm (GA), Hybrid Particle Swarm Optimization algorithm (HPSO), Geospatial Information System (GIS) and Analytic Hierarchy Process (AHP) have been used for selecting proper sites of hospital and allocating the demanded locations to these centers in District 2 of Tehran.
 
Materials & Methods
The main goal of this research is to compare and evaluate the performance of the Genetic Algorithm (GA) and Hybrid Particle Swarm Optimization algorithm (HPSO) for determining the optimal locations of hospital centers and allocating the population blocks to them. In order to limit the search space, the analyzing capabilities of the Geospatial Information System (GIS) and Analytic Hierarchy Process (AHP) have been used to select the candidate sites satisfying the initial conditions and criteria. The locations of such candidate centers are the input of the optimization section. The accuracy of the entire process strongly depends on the selection of these candidate sites. Hence, in this paper, the Analytic Hierarchy Process (AHP) method has been used to select the candidate centers. Then, two optimization algorithms were applied in choosing six optimum sites from the candidate locations and allocating the population to them through minimizing the overall distances between the centers and their allocated blocks. In this study, to improve the Particle Swarm Optimization, a simple neighborhood search has been proposed for better exploitation of the elite particles. The main purpose of this neighborhood search is to increase the convergence rate of the algorithm without decreasing the random search. Since the neighborhood search has a specific definition proportional to each issue, and the issues of location and allocation are spatial issues as well, therefore, the geographic principle of appropriate distribution of the centers in space has been used to define the neighborhood search (the distance between the centers should not be less than a certain amount). In an elite particle, two centers with the lowest distance are selected and one of them is replaced by a new and randomly selected center. If such a change provides a better objective function, the newly created solution in the elite particle is replaced. To calibrate the algorithms parameters, a simulated data set has been used. Having proper values for those parameters, the algorithms were tested on the real data of the study area.
 
Results & Discussion
Given the results of algorithms on real data, the performances of both algorithms are highly dependent on the initial population and the allowed number of iterations. In general, lower numbers of iterations and more populations brings better results than the higher iterations and lower populations. The results show that the Hybrid Particle Swarm Optimization (HPSO) has better performance than the Genetic Algorithm (GA). The convergence rate of the Hybrid Particle Swarm Optimization (HPSO) algorithm is faster than the genetic algorithm (GA), which can be attributed to the particle’s motion toward the best personal and global experiences. Furthermore, the proposed neighborhood search has caused the HPSO algorithm to converge earlier. To evaluate the repeatability of the algorithms, they were performed 40 times for both simulated and real data. Both algorithms have displayed high levels of repeatability, but the Hybrid Particle Swarm Optimization (HPSO) algorithm is more stable. However, the use of Genetic Algorithm (GA) on simulated data has shown more stability than its use on real data. For both the simulated data and real data, the Hybrid Particle Swarm Optimization (HPSO) algorithm performs faster than the Genetic Algorithm (GA). 
 
Conclusion
Simplicity and repeatability of the algorithm are among the important factors which are very significant from the user’s point of view. In this research, the HPSO algorithm has not only been repeatable and simple, but has performed faster than the GA. Therefore, considering these criteria, regarding the special case of this research, the HPSO seems to be more promising than the GA.